Recent advances in sequencing technology is enabling fast and cost-effective generation of sequence data. Soon, whole-genome sequencing will become a routine assay, opening up new opportunities for biomedical research and related fields. The overall objective of this proposal is to develop accurate, scalable computational methods for whole-genome variation study, both by developing a new theoretical framework for studying population genetics models and by improving the key mathematical component underlying various statistical tools for genome analysis. A common thread that runs through this proposal is recombination. Both crossover and gene conversion recombinations will be considered. The specific aims of the proposed research are: (1) Develop and apply a new theoretical framework that complements the standard coalescent theory when the rate of recombination is moderate to large, thus providing a new set of useful analytic tools to the population genomics community. (2) Devise principled methods to derive accurate multi-locus conditional sampling distributions directly from the underlying population genetics model. Improve the accuracy of a wide range of statistical methods for genome analysis that utilize conditional sampling distributions. (3) Develop scalable computational methods for joint estimation of crossover rates, gene conversion rates, and mean conversion tract lengths from population SNP data. Incorporate realistic biological scenarios into a model with overlapping gene conversions and extend the model to handle ectopic (or non-allelic) gene conversions in multigene families. The above goals will be achieved not by engineering modifications based on intuition or simulations, but by applying and generalizing recent mathematical results that are rigorous and accurate. The new theoretical framework developed in this research will allow one to carry out analytic computation, which was considered to be intractable in the standard coalescent theory with recombination. Furthermore, mathematically justified approximations based on diffusion processes will be devised and portable software packages will be developed for population genomics analysis.